mediation analysis

Question 1

mediation analysis

Answer 1

Mediation analysis explores how or why an independent variable (X) influences a dependent variable (Y) through an intermediary variable (M) called the mediator

X → M → Y

The mediator transmits the effect of X on Y

Question 2

mediation model

Answer 2

TRIANGLE WITH ARROWS
M
X Y

(two arrows stick out AWAY from X; M–> Y)

X –> M = path a
M –> Y = path b
X –> Y = path c
X –> Y (controlling M) = path c’

Question 3

path a (mediation model)

Answer 3

effect of X on meditator M

Question 4

path b (mediation model)

Answer 4

effect of M on outcome Y (controlling for X)

Question 5

path c (mediation model)

Answer 5

total effect effect of X on Y (NOT controlling for M)

Question 6

path c’ (mediation model)

Answer 6

direct effect of X on Y (controlling for M)

Question 7

Baron and Kenny (1986) Approach

Answer 7

Step by step procedure to test mediation using a series of regression models

4 steps!

Question 8

steps to Baron and Kenny (1986) Approach

Answer 8

1. Test total effect (Path C): shows that X significantly affects Y
2. Test Path A: Show that significantly affects the mediator M
3. Test Path B (and C): Show that M significantly affects Y when controlling for X
4. Check direct effect (Path C’): check if X still affects Y after controlling for M

Question 9

contemporary approaches vs Baron and Kenny (1986) Approach

Answer 9

Baron and Kenny: If there is no relationship between X and Y, you can’t run mediation analysis

Contemporary thoughts: You can still run a meditation if there no relationship between X and Y

Question 10

STEP 1 (B&K)

Answer 10

1. Test total effect (Path C): shows that X significantly affects Y

Y = B0+ B1(X) + E

Question 11

STEP 2 (B&K)

Answer 11

2. Test Path A: Show that significantly affects the mediator M

M = B0+ B2(X) + E

Question 12

STEP 3 (B&K)

Answer 12

3. Test Path B (and C): Show that M significantly affects Y when controlling for X

Y = B0+ B4(X) + B3(M) + E

Question 13

STEP 4 (B&K)

Answer 13

4. Check direct effect (Path C’): check if X still affects Y after controlling for M

Complete mediation: c’ drops to zero/non-significance

Partial mediation: c’ is reduced but still significant

The sobel test

Question 14

the sober test

Answer 14

formally tests whether the indirect effect (a x b) is significant

Formula: tests if the product of paths a and b differs from zero

Question 15

interpretation of sobel test

Answer 15

If z is significant (p < 0.05), the indirect effect is significant

Provides statistical evidence that M mediates the X → Y relationship

Question 16

limitation of sobel test

Answer 16

Assumes the indirect effect is normally distributed (often not true with small samples)

The product of two normally distributed variables (like a and b) is not normally distributed → it’s skewed
Skewness means the Sobel z-test often has low power (misses real mediation effects) and its confidence intervals can be biased (too narrow!)

Question 17

bootstrapping

Answer 17

step 3 of B&K

Bootstrapping solves the problem of non-normality of the indirect effect (a x b) by empirically estimating its sampling distribution

Question 18

how does bootstrapping work

Answer 18

1. Resample the data many times
2. Re-estimate paths a and b for each sample
3. Compute the product a x b each time
4. After many repetitions, build a bootstrap distribution of the indirect effect
5. Derive confidence intervals directly from the empirical distribution → no normally assumption needed

If 0 not in CI → significant mediation

Question 19

Baron & Kenny: Key Assumptions

Answer 19

Casual order: X → M → Y reflects true causal direction

No unmeasured confounders: no omitted variables affecting M and Y

No measurement error: variables measured without significant error

Linearity and additivity: linear relationships, no X-M interactions

Violations threaten mediation inferences

Question 20

Baron & Kenny: Advantages

Answer 20

Conceptually intuitive and essay to implement

Widely popular – dominant strategy for decades

Systematic approach – think through each link

Clear terminology – full vs partial mediation

Question 21

R Studio Interpretation
of mediation significance

Answer 21

If ACME is significant, you have evidence of mediation

This alone does not tell you whether the mediation is partial or complete

To decide partial vs complete: look at ADE (DIRECT EFFECT)
If ADE is still significant, → partial mediation (some direct effect remains)
If ADE is not significant, → complete mediation (effect passes entirely through M)

Question 22

Baron & Kenny: Limitations

Answer 22

1. No direct test of indirect effect (a x b)
2. Requires significant total effect (step 1) – can miss suppression
3. Dichotomous thinking – full vs partial mediation
4. Single mediator focus – doesn’t handle multiple mediators well
5. No measurement error correction
6. Causal inference concerns – doesn’t prove causality

Question 23

Modern Approaches: Why We Need Them

Answer 23

Key problems with Baron & Kenny:
- Focus on individual path significance, not indirect effect
- Can miss mediation when direct/indirect effects cancel out
- Assumes normality of indirect effect distribution
- Limited to simple models

Modern solutions:
- Direct testing of indirect effects
- Bootstrapping for non-normal distributions
- SEM for complex models
- Focus on effect sizes, not just significance

Question 24

Modern SEM Approach to Mediation - key features

Answer 24

Unified model estimation: single model instead of separate regressions

Direct test of indirect effect: explicitly define a x b as parameter

Handles complex models: multiple mediators, latent variables

Measurement error correction: account for unreliability

Question 25

advantages of modern SEM approach

Answer 25

Simultaneous estimation of all paths Can include latent variables Model fit evaluation Handles missing data

Question 26

SEM: Direct Testing of Indirect Effects

Answer 26

Modern approach focuses on: - Significance of a x b (not individual paths) - Confidence intervals for indirect effect - Effect sizes and proportion mediated - Bootstrapping for non-normal distributions Skip Baron & Kenny Step 1 if theory justifies mediation!

Question 27

SEM model fit indices and model comparison

Answer 27

X^2 test: non-significant = good fit CFI/TLI: >_ 0.95 excellent, >_0.90 acceptable RMSEA: <_0.05 close fit, <0.08 reasonable SRMR: <0.08 good fit model comparison: Test full vs partial mediation Compare with/without direct path X^2 difference tests

Question 28

Why Bootstrapping (advantages)

Answer 28

a × b often has skewed distribution (not normal) Sobel test assumes normality → low power Bootstrap makes minimal assumptions

Question 29

SEM: Advantages Over Baron & Kenny

Answer 29

Direct test of indirect effect with confidence intervals Handles complex models (multiple mediators, latent variables) Accounts for measurement error Model fit evaluation and comparison Bootstrapping for robust inference Effect size reporting (proportion mediated)

Question 30

SEM: limitations

Answer 30

Larger sample size requirements More complex to implement and interpret Software knowledge needed Still assumes causality (design issue, not statistical)